Slitherlink

Slitherlink (also called Fences, Loop the Loop, or Dotty Dilemma) is a logic puzzle played on a grid of dots. The player must draw a single continuous loop along the edges of the grid — connecting dot to dot — without crossing or branching. Some cells contain a number (0 to 3) indicating how many of that cell's four edges are part of the loop. The challenge is to find the one loop that satisfies all the number clues.

Rules

1. Draw a single closed loop by connecting adjacent dots with horizontal or vertical line segments.
2. The loop must not cross itself or branch — every dot on the loop has exactly two segments connected to it.
3. A number inside a cell indicates how many of that cell's four edges are used by the loop.
4. Cells without a number can have any number of edges (0 to 4) used by the loop.
5. There is exactly one valid loop.

Number Meanings

• 0: None of the cell's four edges are part of the loop. The loop goes completely around this cell.
• 1: Exactly one edge of this cell is part of the loop.
• 2: Exactly two edges of this cell are part of the loop.
• 3: Three of this cell's four edges are part of the loop. Only one edge is not used.

Strategies

• 0 Cells: All four edges are excluded. Mark them with an "x" to track eliminated edges.
• 3 Cells: Three of four edges must be loop segments. The corners of a 3-cell have strong constraints — if two 3-cells are adjacent, the shared edge must be part of the loop, and specific patterns are forced.
• Adjacent 3-3: Two adjacent 3-cells always force the shared edge to be a loop segment, plus specific edges around both cells in a predictable pattern.
• Adjacent 3-0: A 3 next to a 0 forces specific edges: the three loop edges of the 3-cell must be the ones not shared with the 0-cell.
• Corner Cells: Cells in the corners of the grid have only two possible edges in certain directions, limiting the loop path significantly.
• Connectivity: The loop must be a single closed curve. If placing a segment would create a small closed loop leaving numbered cells unsatisfied, that segment is invalid.
• Parity Arguments: At each dot, either zero or two segments meet. If one segment is confirmed at a dot, exactly one more must also be present.

Slitherlink was invented by Nikoli, the legendary Japanese puzzle publisher, and first appeared in *Puzzle Communication Nikoli* in 1989. It was one of several loop-drawing puzzles that Nikoli developed during a highly creative period in the late 1980s and early 1990s.

The English name "Slitherlink" captures the feel of the puzzle — the loop "slithers" between the dots, linking them into a closed path. In Japan, the puzzle is known by several names including "Suriza" (a transliteration) and the descriptive "Ruupu" (Loop). Other common English names include "Fences" and "Loop the Loop."

Slitherlink became an internationally recognized puzzle through the World Puzzle Championship, where it has been a regular fixture since the mid-1990s. It is considered one of the canonical WPC puzzle types and appears in nearly every year's competition. The puzzle's popularity in competitive puzzling led to its adoption by newspapers and puzzle magazines outside Japan.

The puzzle occupies a unique niche among grid puzzles because the solver draws lines rather than placing numbers. This gives Slitherlink a different visual and tactile character compared to Sudoku-like puzzles. The logical techniques required — especially loop connectivity arguments and parity reasoning — exercise different mental muscles than number-placement puzzles. The resulting loop itself can have an aesthetically pleasing, organic shape, giving completed Slitherlink puzzles a visual appeal similar to completed nonograms. Slitherlink appears in Simon Tatham's Portable Puzzle Collection and in numerous puzzle apps, and maintains a devoted following among puzzle enthusiasts worldwide.